School within both Princeton and Carleton?

ETON

Think of a prestigious British boarding school known for its distinctive uniform and alumni like princes, which shares its name with a college at both Princeton and Carleton universities.

This clue plays on the idea of a "school" being hidden inside the names of two universities. "Princeton" contains "ETON" (PRINCETON) and "Carleton" also holds "ETON" (CARLETON), so the answer is the famous British boarding school Eton College. It’s a clever "hidden word" puzzle where the same answer fits inside both names.